The Perkins Elementary School in South Boston is barely visible behind rows of nondescript brick buildings inside the Old Colony public housing development. Students make do without the most basic amenities, eating breakfast and lunch at their desks, taking gym classes at a Boys & Girls Club, and checking out books at a neighborhood library.

Pat Greenhouse/Globe Staff

Holland school students can use an indoor pool and enjoy other advantages.

About three miles away in a crime-ridden Dorchester neighborhood, the Holland Elementary School stands like a beacon. Nestled among fruit trees, Holland sports two cafeterias that serve freshly prepared meals, an indoor basketball court, an Olympic-size heated swimming pool, a soundproof music room with red and white electric guitars, and a library with more than 7,000 books.

The stark differences between these two schools extend well beyond their facilities. Perkins, with its bare-bones surroundings, often propels students in early grades to great academic heights on standardized tests, while Holland struggles to get students to understand reading and math fundamentals.

Across Boston, astonishing inequities exist among the 78 city-run early-education centers, elementary schools, and K-8 schools, according to a Globe analysis of their test scores, facilities, and programs. The conclusions offer a rare glimpse into the state of the city’s public schools:

- Half were built between 1896 and 1932, and many buildings lack basic amenities. Four don’t have cafeterias; 22 schools lack auditoriums; 30 are without gymnasiums; and 59 schools, three-quarters of those surveyed, do not have athletic fields.

- An impressive facility often does not equate with a stellar academic program. Other schools with meager facilities, such as Bradley in East Boston, Hale in Roxbury, and Mozart in Roslindale, had some of the highest reading and math scores on last spring’s Massachusetts Comprehensive Assessment System exams in the third grade. By contrast, some schools with swimming pools - such as Hennigan in Jamaica Plain, Marshall in Dorchester, and Mildred Avenue in Mattapan - landed in the bottom.

- Despite their popularity, smaller schools don’t necessarily outperform larger ones. Although small schools tend to dominate the top rankings in MCAS, the School Department in June closed several small schools, such as Farragut in Mission Hill and Emerson in Roxbury, due to poor performance.

The disparities add an agonizing layer to the school-selection process, underway for the next school year, as parents weigh what matters most for their child’s education and happiness: A nice building or solid academics? An outstanding music program or rigorous science instruction? A school near home or one with an after-school program?

. . .

THE UNEVEN distribution of great facilities and programs underpins Boston’s elaborate school-lottery system, which was designed to give students a chance of getting into the best schools, and is also the reason the process is so harrowing. Some students win, gaining access to one of the city’s best schools, while other deserving students are consigned to schools with poor records of achievement, substandard facilities, or both.

“The reality is there are not enough good schools,’’ said Kim Janey, senior project director for the Boston School Reform Initiative at Massachusetts Advocates for Children, a Boston nonprofit.

“People put all their hopes and dreams in their children’s education. That’s why not getting one of their [school] choices is so hard, because the alternative is not something you can live with,’’ said Janey, who believes the superintendent is working hard to remedy academic and achievement disparities.

To improve equity among the city’s schools, Superintendent Carol R. Johnson has pursued an aggressive overhaul of schools, setting ambitious performance goals that often exceed state averages.

The plan has led to the closure of nearly a dozen elementary schools because of poor performance, the expansion of several successful schools, and the designation of a large swath of schools in Dorchester, Roxbury, and Jamaica Plain - areas stricken with immense poverty and too many low-achieving schools - for intensive intervention.

But too few schools are rising to the challenge, according to the Globe analysis.

To ensure more students are skillful readers by fourth grade - when students must tackle more challenging material in a variety of subjects, such as science and math - Johnson instituted a new reading program two years ago and added two key benchmarks to monitor progress along the way.

But less than three dozen schools last spring met Johnson’s goal of having at least 75 percent of their first-graders reading at grade level, according to a Globe review of scores from the Dynamic Indicators of Basic Early Literacy Skills, a standardized test that measures a student’s knowledge of phonics and other reading skills.

Performance was even worse in the third grade. Only Perkins and three other schools met or exceeded Johnson’s goal of having 72 percent of students score proficient in reading on the MCAS.

Two dozen schools had less than a quarter of their third-graders reaching proficiency.

In an interview, Johnson acknowledged the uneven quality of academic achievement and facilities and stressed that more work remains to provide “excellence and equity’’ to every student across the district.

“I think we can achieve equity, but we will have to make some tough decisions about how to direct the resources we have to help students off track to catch up, and at the same time not shortchange the students who are already on track and could achieve even more,’’ Johnson said.

“This is not a game of winners or losers. The real issue for us, and the country, is making sure every single student has the best chance at the best education possible.’’

. . .

CREATING EQUITY - an issue so deeply interwoven in the desegregation of schools nationwide - has dogged urban school leaders for decades.

In Massachusetts, small cities such as Malden demolished their old elementary and middle schools about a decade ago and replaced them with K-8 schools designed to offer similar programs and amenities.

But in Boston such a dramatic reconstruction of schools would be too costly. The city has built less than two dozen early-education centers, elementary schools, and K-8 schools in the last four decades.

Johnson said it is not coincidental that some of the city’s newer buildings have among the worst academic records.

Many of the newer schools, including those built as far back as the 1970s, are in distressed neighborhoods where the need to overhaul public education has been the greatest.

Some of these schools, including Holland, are slated for drastic restructuring, in hopes of raising the quality of its academic programs to the same caliber as its facilities.

“A positive environment can make students feel more excited and happy about being in school, but we as a school need to do a better job at creating more students who can perform at proficient levels,’’ said Jeichael Henderson, principal of the Holland Elementary School, on Olney Street.

Henderson is trying to raise academic performance by changing math and reading instruction, providing teachers with more training and classroom preparation time, and offering more tutoring to students.

But finding success in a building with nearly 800 students - half of whom speak a language other than English - has proved difficult. And even if a rebound occurred, Henderson said, many parents may be reluctant to send their children to a school in a neighborhood that has seen about a half-dozen homicides since June.

As it is, when students start doing well at the school, parents often seek a transfer to another public or private school with a reputation for academic rigor, he said.

“People feel threatened by the community,’’ Henderson said.

. . .

BOSTON HAS HAD greater success in turning around small schools, often located in older facilities. While the smallness increases the odds of success, the schools also share other traits: an inspirational principal, devoted teachers, and tenacious parents committed to changes.

The number of good schools has risen over the last decade, said Laura Perille, executive director of EdVestors, a Boston nonprofit that has recognized six Boston schools in recent years for making dramatic gains on the MCAS.

“There are schools across the district that can and are making the changes,’’ Perille said. “But the work is not finished.’’

Turning around a low-achieving school can seem daunting at first.

When Barney Brawer became principal of Perkins in 2005, the school of about 200 students was under a state mandate to reverse years of dismal academic performance that had prompted many parents to shun the school.

Pat Greenhouse/Globe Staff

When Barney Brawer became principal at Perkins in 2005, the South Boston school was under a mandate to reverse its dismal academic performance.

Over the past six years, Brawer said, the school carefully rebuilt its reading and math programs and injected new life in other subjects. To promote better physical well-being among students, for instance, the school painted a blue walking track around its building, built a new playground, and created an outside classroom for science lessons.

. . .

THE OVERHAUL is not a complete success yet. Although students do well in the early grades, performance slides off notably in the fourth and fifth grades, as the school’s more talented students transfer to private schools or to other public schools that offer specialized programs to help students gain admission to the city’s competitive exam schools.

Some staffers say they wish their building could provide some basic venues, such as a cafeteria.

In a first-grade classroom last month, about two dozen students ate chili, beans, and rice at their desks, which were covered by placemats brought in by their teacher, Melissa Leverett-King.

“When they are in their classroom all day, it’s like they are prisoners in their desks,’’ said Leverett-King, noting that setting up for breakfast and lunch and cleaning up afterward cuts into precious minutes of instructional time.

But at the same time, Leverett-King said she is enchanted by the historical character of the building, such as the creaky hardwood floors, marble walls, and student coat racks and cubby holes concealed under pull-down wooden doors.

Brawer said he is hoping to gain additional space for the school by leasing a soon-to-be-vacant building next door that has been housing Head Start.

As Tarso Ramos, a Roxbury father, scouted schools at one of the city’s annual “showcase of schools,’’ held last month at a Jamaica Plain school, he had already conceded that he and his wife may not find the dream school for their son.

“It’s like a series of trade-offs,’’ Ramos said of the school-selection process. “So you figure out the right mix and what you can live without.’’

James Vaznis can be reached at jvaznis@globe.com. Follow him on Twitter @globevaznis. Matt Carroll of the Globe staff contributed to this report.

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